Backlund transformations : exact solutions for the KdV and the Calogero-Degasperis-Fokas mKdV equationsBacklund transformations : exact solutions for the KdV and the Calogero-Degasperis-Fokas mKdV equations

The exact solutions for the KdV and the Calogero-Degasperis-Fokas mKdV equations can be obtained by the AKNS class. The technique developed relies on the construction of the wave Functions which are solutions of the associated AKNS system; that is, a linear eigenvalue problem in the form of a system of first order partial differential equations. The method of characteristics is used and Backlund transformations (BTs) are employed to generate two new solutions from the old. (C) 1998 B. Teubner Stuttgart-John Wiley & Sons Ltd.